A family of warped product semi-Riemannian Einstein metrics

2015/08/17 by Pina, Romildo, de Sousa, Marcio Lemes
#Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1508.03880

Abstract

We study warped products semi-Riemannian Einstein manifolds. We consider the case in that the base is conformal to an n-dimensional pseudo Euclidean space and invariant under the action of an translation group. We provide all such solutions in the case Ricci flat when the base is conformal to an n-dimensional pseudo-Euclidean space, invariant under the action of an translation group and the fiber F is Ricci flat. In particular, we obtain explicit solutions, in the case vacuum, for the Einstein field equation.

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